Water: Frequently Asked Questions

How can a liquid have a structure?
Does the radial distribution peak at about 3.7 Å exist?
Is there fine structure in the radial distribution function?
Are there interstitial water molecules?
Are the icosahedral clustering model and the outer structure two-state mixture models related?

How can a liquid have a structure?

Structure, when applied to liquids [572 ] has a different meaning to when it is applied to solids. In liquids the molecules must have constant translational motion but they may travel in relatively unchanging non-crystalline clusters, containing many water molecules, with far lower hydrogen bond disruption. Additionally, any rotation of such clusters results in translation of the individual molecules. Although this requires that long-range order is lost, there is still some short-range order. This short-range order has been found to extend to at least 8 Å radius even with totally inert, non-polar and spherically symmetrical molecules such as in liquid argon [95], and up to 15 Å radius (equal to the proposed ES structure) in the more-ordered supercooled heavy water (D₂O) [221]. The distance over which this short-range order exists should be greater when there is extensive hydrogen bonding as in water. This has been confirmed in aqueous dipole moment calculations where water 10 Å distant still contributes significantly [452 ]. In simulations, even where the orientation of individual water molecules is rapidly lost, coherent patterns of extensive hydrogen bonding have been found to exist for periods lasting throughout the simulation [329]. In liquids, the X-ray (and neutron) diffraction pattern corresponds to the time-averaged positions (with exposure times for X-ray studies many orders of magnitude longer than the longest simulation) of the molecules within the volume corresponding to the potential range of this short-range order and so can give valid information as to the preferred structuring of these molecules. An alternative way of looking at this structure is as the average, directionally correlated, structure around the water molecules taken from an extremely large pool of liquid water molecules; many orders of magnitude greater than used in simulations. In this context it is relevant to note that the relative positioning of water molecules around cations such as Ca²⁺ remain close to fixed essentially forever but with individual water molecules exchanging with the bulk in less than a nanosecond. Also hexagonal ice remains firmly ordered and crystalline in spite of constantly and rapidly breaking and changing its hydrogen bonding. There is evidence that water structuring may change over periods of time of greater than seconds [631 ] or days [1102 ] or, in other studies, at least 10¹⁶ times greater than the lifetime of a single hydrogen bond [4, 509 , 1148]. Another study shows that disturbances in the structure of single water molecules may last only 50 femtoseconds, due to the rapid redistribution of energy amongst the cluster hydrogen bonds [750 ]. Thus the structure determined for water depends on the time- and size-scales over which it is determined.

It is also possible that there may be more than one stable or metastable liquid structure coexisting in equilibrium at the same time. This has been shown for several materials including mixed oxide melts [768 ], liquid sulfur [769 ] and liquid phosphorus [770 ]. Note also that there are many instances where two liquid water phases coexist in aqueous biphasic systems. [Back to Top ]

Does the radial distribution peak at about 3.7 Å exist?

There still seems doubt in the minds of some workers as to whether the radial distribution peak at about 3.7 Å really exists, in spite of the need for water molecules at about this distance in order to give water a higher density than ice. Narten et al [9] first reported this peak and explained it in terms of the presence of interstitial water molecules within ice Ih type hexameric boxes. He later put this peak down to artifactual ripples due to the early termination of a Fourier integral [58] and therefore having no structural significance. The peak was later again observed in his neutron diffraction data [35]. The X-ray data has more recently been reanalyzed and the peak is still present [59], as it is in some simulation studies [7, 66] and in neutron diffraction of effectively-powdered hexagonal ice [154]. It has also been shown to grow with increasing temperature [50] and pressure [51]. Four water molecules are generally found roughly tetrahedrally placed in supercooled water at distances about 2.78 Å. The position of the fifth nearest water molecule has been found using simulations and appears maximally at about 3.8 Å and 3.0 Å, in relative amounts dependent on the density [1055 ]. It is now the majority view of researchers in the field that water molecules exist at these intermediate distances in liquid water under ambient conditions where they would be at about the expected distance for non-hydrogen bonded inner sphere water molecules. [Back to Top ]

Is there fine structure in the radial distribution function?

The data obtained by both X-ray and neutron diffraction (for a recent review, see [392 ]) are subject to uncertainties. The oxygen atom radial distribution function is obtained from neutron diffraction data by subtraction of the hydrogen (deuterium) intensities, thereby giving rise to noise, which when smoothed leaves only the major features. Also, neutron diffraction data is generally analyzed ignoring any inherent differences in the water structuring between D₂O, HDO and H₂O and therefore will produce less detail as these structures differ significantly. Even small differences in the H₂O content of D₂O give rise to very different radial distribution functions [715 ], a problem made worse at low temperatures. There are reasons to suppose that mixed D₂O, HDO and H₂O solutions are not perfectly homogeneous. It is particularly noticeable that the reported oxygen atom radial distribution functions, determined from neutron diffraction data, differ considerably from each other. Also, the structure of identically produced low density amorphous ices of D₂O and H₂O are not identical, even allowing for a temperature shift [940 ]. A useful review of these techniques has been published [916 ].

X-ray diffraction is sensitive to the concentration of electrons. During analysis, these are assumed to be spherically distributed but, as the molecule is not spherically symmetrical, clearly this is an approximation. However, the electron densities around the hydrogen atoms are displaced somewhat towards the oxygen atoms. Also, the electron distribution around water molecules in liquid water appears to be more spherical than in the gas phase [90] and any residual effects this causes are largely confined within the nearest-neighbor shell [59]. The data (for the radial distribution function of water) is not subject to the same amount of noise (and required smoothing) as with neutron diffraction and therefore intrinsically capable of showing a greater degree of fine structure (see for example the comparison of X-ray and neutron diffraction data given in [888 , 1245 ]). Although the fine structure in the X-ray data of Narten [9] was later interpreted [58] by the author as 'ripples' due to the data processing, the key peak at 3.7 Å has now been established beyond question. It seems as if such 'ripples' are of importance mainly below 2.5 Å. An X-ray scattering experiment at 27 °C reported far less fine structure [199] but the higher temperature may be responsible as recent work at lower temperatures certainly does show fine structure out beyond 1 nm [1476]. [Back to Top ]

Are there interstitial water molecules?

The term 'interstitial' can have several meanings. Historically it meant unbonded or weakly hydrogen-bonded water molecules sitting in the empty spaces in a tetrahedrally bonded network, such as within the hexameric boxes in ice Ih structures [9] (this is the meaning that is generally used in this site). More recently the term has been used to describe water molecule in the 3.7 Å peak of the oxygen radial distribution function. They may be in this position because they are not hydrogen bonded, because they are tetrahedrally hydrogen bonded but in a separate local cluster or because they are hydrogen bonded within the same local cluster but where there is considerable bond bending involved. These definitions are not necessarily mutually exclusive. It is not the case that interstitial molecules must have no hydrogen bonds; it being quite possible that such a molecule can have a number of normal or somewhat distorted hydrogen bonds. The idea of interstitial molecules has recently been re-introduced using the evidence of some simulation studies [66] and the neutron diffraction finding of interstitial water in effectively-powdered hexagonal ice [154]. When liquid water is put under pressure, there appears to be an increase in interpenetration of hydrogen bonded networks at about 200 MPa (at 290 K) as evidenced from the increase in O····O nearest molecule separation distances, and O-H stretch vibration frequency, with pressure between about 200 to 400 MPa [533 ]. Both isoelectronic neon and the larger argon atoms can be found in interstitial sites in hexagonal ice, proving they have sufficient size to contain water molecules. Ice-seven and ice-eight both consist of interpenetrating networks where all water molecules effectively occupy interstitial sites. [Back to Top ]

Are the icosahedral clustering model and the outer structure two-state mixture models related?

The outer structure two-state mixture model has been successfully used to explain many of the anomalous properties of water (for example, [23, 56, 57, 60, 69, 73, 148, 826 ]). Although this model explicitly includes ice Ih (hexagonal ice) and ice-two (ice II) substructures, these may be thought of as representing fully tetrahedral open low-density structures (ice Ih equivalent in the icosahedral network model to ES) and tetrahedral structures with close second neighbors, giving a higher density 'collapsed' structure (ice-two equivalent in the icosahedral network model to CS). This equivalence can best be envisioned by examining the behavior of a 'c'-type water molecule. They are the most numerous water molecules in icosahedral water clusters (120/280 = 43%) and they are the least affected by the movements due to the ESCS equilibrium. These water molecules are tetrahedrally hydrogen-bonded to the surrounding four (2 'b' and 2 'c' type) water molecules in both ES and CS. In ES the next 'outer' structure (including 2 'a' type) water molecules are also tetrahedrally positioned but in CS the two 'a' type water molecules in this 'outer' structure are flexible and collapsed, allowing close second neighbors. It may be noted that the outer structure two-state mixture model does not depend on the explicit structures of ice Ih and ice-two in order to explain water's anomalous properties; in fact the existence of such explicit structures is unlikely as shown by many of the other properties of water (for example, see earlier). This means that arguments using this model can also be used in support of the icosahedral cluster model (but not explicitly vice versa). [Back to Top ]